We analyze the impact of price stability-oriented monetary strategies (inflation targeting - IT - and constraining exchange rate arrangements) on inflation persistence using a timevarying coefficients framework in a panel of 68 countries (1993-2013). We show that explicit IT has a stronger effect on taming inflation persistence than implicit IT and is effective even during and after the financial crisis. Regimes with the U.S. dollar as a reserve currency are less effective than those using the Euro; this effect correlates with the level of the reserve currency's inflation persistence. Further, we document the existence of structure in inflation persistence data. Our results are robust to differences in four well established inflation persistence measures and are not affected by existing structural breaks or the endogeneity of monetary strategies.